CH$4$ Q$4\mathrm{.}5$ Ethical Considerations. Take a look back at Example $4\mathrm{.}6.$ Is it deceptive

advertising? Is it unethical to advertise a future value like this without a disclaimer?

EXAMPLE $4\mathrm{.}6$ Deceptive Advertising

Recently, some businesses have been saying things like "Come try our product. If you do$,$

we'll give you $$100$ just for coming by$!"$ If you read the fine print, what you find out is that they

will give you a savings certificate that will pay you $$100$ in $25$ years or so$.$ If the going interest

rate on such certificates is $10$ percent per year, how much are they really giving you today?

What you're actually getting is the present value of $$100$ to be paid in $25$ years. If the

discount rate is $10$ percent per year, then the discount factor is:

$\frac{1}{1\mathrm{.}125}=\frac{1}{10\mathrm{.}8347}=\mathrm{.}0923$

This tells you that a dollar in $25$ years is worth a little more than nine cents today, assuming

a $10$ percent discount rate. Given this, the promotion is actually paying you about $\mathrm{.}0923$$$100=$

$$9\mathrm{.}23.$ Maybe this is enough to draw customers, but it's not $$100.$

CH$4$ Q$6$ Calculating Rates of Return. Assume the total cost of a college education will be

$$280,000$ when your child enters college in $18$ years. You presently have $$45,000$ to invest. What

annual rate of interest must you earn on your investment to cover the cost of your child's college

education?

CH$4$ Q$9$ Calculating the Number of Periods. You're trying to save to buy a new $$150,000$

Ferrari. You have $$35,000$ today that can be invested at your bank. The bank pays $3\mathrm{.}2$ percent

annual interest on its accounts. How long will it be before you have enough to buy the car?

CH$5$ Q$5\mathrm{.}6$ Present Value. Suppose two athletes sign $10-$year contracts for $$80$ million. In one

case, we're told that the $$80$ million will be paid in $10$ equal installments. In the other case, we're

told that the $$80$ million will be paid in $10$ installments, but the installments will increase by $5$

percent per year. Who got the better deal?

CH$5$ Q$22$ Calculating EAR. Friendly's Quick Loans, Inc., offers you "Five for four, or I

knock on your door." This means you get $$4$ today and repay $$5$ when you get your paycheck in

one week $($or else$).$ What's the effective annual return Friendly's earns on this lending business? If

you were brave enough to ask, what APR would Friendly's say you were paying?

CH$5$ Q$47$ Annuity and Perpetuity Values. Mary is going to receive a $30-$year annuity of

$$10,500.$ Nancy is going to receive a perpetuity of $$10,500.$ If the appropriate interest rate is $7$

percent, how much more is Nancy's cash flow worth?